Saving changes doesn’t work on custom plugin admin page

I try to call this plugin from admin page of my plugin.
I can view and edit the referred table, but saving the changes does not happen. Ajax call passes successfully but DB table is not updated.

There is saying my-plugin/settings.php page in WP admin interface, where I do:

$table='wp_my_table';
if(function_exists('add_db_table_editor')){
  add_db_table_editor(array(
   'title'=>'My title',
   'table'=>$table,
   'sql'=>"SELECT * FROM $table ORDER BY class_id ASC",
   'id_column'=>'class_id',
   'cap'=>'manage_options',
   'columnNameMap'=>Array(................),
   'default_values'=>Array(................)
  ));
  print(dbte_shortcode(Array('id'=>$table)));
}

This displays the DBTE interface.

Then, when I do some changes and hit ‘Save changes’ button, the following ajax call happens:

"page":"my-plugin/settings.php",
"action":"dbte_save",
"data":"{seem to be correct JSON data}",
"table":"wp_my_table"}

I am confused by the fact that “page” here is referring back to the page where the editor is displayed. Should it refer to some DBTE component instead?

Do I miss some step that binds the frontend interface to DBTE backend?